Can you complete this jigsaw of the multiplication square?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

If you have only four weights, where could you place them in order to balance this equaliser?

Here is a chance to play a version of the classic Countdown Game.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Can you hang weights in the right place to make the equaliser balance?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Use the number weights to find different ways of balancing the equaliser.

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

An interactive activity for one to experiment with a tricky tessellation

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

How many different rhythms can you make by putting two drums on the wheel?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Move just three of the circles so that the triangle faces in the opposite direction.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Train game for an adult and child. Who will be the first to make the train?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Can you find all the different ways of lining up these Cuisenaire rods?

Use the interactivities to complete these Venn diagrams.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.